I actually googled this to see if maybe there was some obscure use of quotation marks as shorthand for a period of time. And there is! Unfortunately, according to Wikipedia (http://en.wikipedia.org/wiki/Hatch_mark), "In regard to time, a single hatch mark indicates minutes and a double hatch mark indicates seconds..." So it *could* be read as indicating that your Grandmother is 93 seconds old, which is still, obviously, incorrect.

Presumably the person was thinking of the convention of using an apostrophe (not "thingies") to abbreviate a date (as in '93 instead of 1993). It reflects how illiterate many people are that she doesn't understand why that works, and all she knows is it has something to do with years.

Good hypothesis Lynn. I thought she might have gotten confused with the convention of using hashmarks to write inches (as the submitter suggested). Your explanation gives a good reason why she'd think punctuation has anything to do with writing years.